
/* @(#)e_rem_pio2.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 *
 */

/* __rem_pio2(x,y)
 *
 * return the remainder of x rem pi/2 in y[0]+y[1]
 * use __kernel_rem_pio2()
 */

#include "fdlibm.h"

#ifdef _NEED_FLOAT64

/*
 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
 */
static const __int32_t two_over_pi[] = {
    0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 0x95993C,
    0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 0x424DD2, 0xE00649,
    0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 0xA73EE8, 0x8235F5, 0x2EBB44,
    0x84E99C, 0x7026B4, 0x5F7E41, 0x3991D6, 0x398353, 0x39F49C, 0x845F8B,
    0xBDF928, 0x3B1FF8, 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D,
    0x367ECF, 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
    0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 0x560330,
    0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 0x91615E, 0xE61B08,
    0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 0x4D7327, 0x310606, 0x1556CA,
    0x73A8C9, 0x60E27B, 0xC08C6B,
};

static const __int32_t npio2_hw[] = {
    0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
    0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
    0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
    0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
    0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
    0x404858EB, 0x404921FB,
};

/*
 * invpio2:  53 bits of 2/pi
 * pio2_1:   first  33 bit of pi/2
 * pio2_1t:  pi/2 - pio2_1
 * pio2_2:   second 33 bit of pi/2
 * pio2_2t:  pi/2 - (pio2_1+pio2_2)
 * pio2_3:   third  33 bit of pi/2
 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
 */

static const __float64
    zero = _F_64(0.00000000000000000000e+00), /* 0x00000000, 0x00000000 */
    half = _F_64(5.00000000000000000000e-01), /* 0x3FE00000, 0x00000000 */
    two24 = _F_64(1.67772160000000000000e+07), /* 0x41700000, 0x00000000 */
    invpio2 = _F_64(6.36619772367581382433e-01), /* 0x3FE45F30, 0x6DC9C883 */
    pio2_1 = _F_64(1.57079632673412561417e+00), /* 0x3FF921FB, 0x54400000 */
    pio2_1t = _F_64(6.07710050650619224932e-11), /* 0x3DD0B461, 0x1A626331 */
    pio2_2 = _F_64(6.07710050630396597660e-11), /* 0x3DD0B461, 0x1A600000 */
    pio2_2t = _F_64(2.02226624879595063154e-21), /* 0x3BA3198A, 0x2E037073 */
    pio2_3 = _F_64(2.02226624871116645580e-21), /* 0x3BA3198A, 0x2E000000 */
    pio2_3t = _F_64(8.47842766036889956997e-32); /* 0x397B839A, 0x252049C1 */

__int32_t
__rem_pio2(__float64 x, __float64 *y)
{
    __float64 z = _F_64(0.0), w, t, r, fn;
    __float64 tx[3];
    __int32_t i, j, n, ix, hx;
    int e0, nx;
    __uint32_t low;

    GET_HIGH_WORD(hx, x); /* high word of x */
    ix = hx & 0x7fffffff;
    if (ix <= 0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
    {
        y[0] = x;
        y[1] = 0;
        return 0;
    }
    if (ix < 0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
        if (hx > 0) {
            z = x - pio2_1;
            if (ix != 0x3ff921fb) { /* 33+53 bit pi is good enough */
                y[0] = z - pio2_1t;
                y[1] = (z - y[0]) - pio2_1t;
            } else { /* near pi/2, use 33+33+53 bit pi */
                z -= pio2_2;
                y[0] = z - pio2_2t;
                y[1] = (z - y[0]) - pio2_2t;
            }
            return 1;
        } else { /* negative x */
            z = x + pio2_1;
            if (ix != 0x3ff921fb) { /* 33+53 bit pi is good enough */
                y[0] = z + pio2_1t;
                y[1] = (z - y[0]) + pio2_1t;
            } else { /* near pi/2, use 33+33+53 bit pi */
                z += pio2_2;
                y[0] = z + pio2_2t;
                y[1] = (z - y[0]) + pio2_2t;
            }
            return -1;
        }
    }
    if (ix <= 0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
        t = _NAME_64(fabs)(x);
        n = (__int32_t)(t * invpio2 + half);
        fn = (__float64)n;
        r = t - fn * pio2_1;
        w = fn * pio2_1t; /* 1st round good to 85 bit */
        if (n < 32 && ix != npio2_hw[n - 1]) {
            y[0] = r - w; /* quick check no cancellation */
        } else {
            __uint32_t high;
            j = ix >> 20;
            y[0] = r - w;
            GET_HIGH_WORD(high, y[0]);
            i = j - ((high >> 20) & 0x7ff);
            if (i > 16) { /* 2nd iteration needed, good to 118 */
                t = r;
                w = fn * pio2_2;
                r = t - w;
                w = fn * pio2_2t - ((t - r) - w);
                y[0] = r - w;
                GET_HIGH_WORD(high, y[0]);
                i = j - ((high >> 20) & 0x7ff);
                if (i > 49) { /* 3rd iteration need, 151 bits acc */
                    t = r; /* will cover all possible cases */
                    w = fn * pio2_3;
                    r = t - w;
                    w = fn * pio2_3t - ((t - r) - w);
                    y[0] = r - w;
                }
            }
        }
        y[1] = (r - y[0]) - w;
        if (hx < 0) {
            y[0] = -y[0];
            y[1] = -y[1];
            return -n;
        } else
            return n;
    }
    /*
     * all other (large) arguments
     */
    if (ix >= 0x7ff00000) { /* x is inf or NaN */
        y[0] = y[1] = x - x;
        return 0;
    }
    /* set z = scalbn(|x|,ilogb(x)-23) */
    GET_LOW_WORD(low, x);
    SET_LOW_WORD(z, low);
    e0 = (int)((ix >> 20) - 1046); /* e0 = ilogb(z)-23; */
    SET_HIGH_WORD(z, ix - ((__int32_t)e0 << 20));
    for (i = 0; i < 2; i++) {
        tx[i] = (__float64)((__int32_t)(z));
        z = (z - tx[i]) * two24;
    }
    tx[2] = z;
    nx = 3;
    while (tx[nx - 1] == zero)
        nx--; /* skip zero term */
    n = __kernel_rem_pio2(tx, y, e0, nx, 2, two_over_pi);
    if (hx < 0) {
        y[0] = -y[0];
        y[1] = -y[1];
        return -n;
    }
    return n;
}

#endif /* _NEED_FLOAT64 */
